457 research outputs found
Sum rules for correlation functions of ionic mixtures in arbitrary dimension
The correlations in classical multi-component ionic mixtures with spatial
dimension are studied by using a restricted grand-canonical ensemble
and the associated hierarchy equations for the correlation functions. Sum rules
for the first few moments of the two-particle correlation function are derived
and their dependence on is established. By varying continuously near
it is shown how the sum rules for the two-dimensional mixture are related
to those for mixtures at higher .Comment: 19 page
Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion
A quantum damped-polariton model is constructed for an inhomogeneous
anisotropic linear dielectric with arbitrary dispersion in space and time. The
model Hamiltonian is completely diagonalized by determining the creation and
annihilation operators for the fundamental polariton modes as specific linear
combinations of the basic dynamical variables. Explicit expressions are derived
for the time-dependent operators describing the electromagnetic field, the
dielectric polarization and the noise term in the latter. It is shown how to
identify bath variables that generate the dissipative dynamics of the medium.Comment: 24 page
Atomic decay near a quantized medium of absorbing scatterers
The decay of an excited atom in the presence of a medium that both scatters
and absorbs radiation is studied with the help of a quantum-electrodynamical
model. The medium is represented by a half space filled with a randomly
distributed set of non-overlapping spheres, which consist of a linear
absorptive dielectric material. The absorption effects are described by means
of a quantized damped-polariton theory. It is found that the effective
susceptibility of the bulk does not fully account for the medium-induced change
in the atomic decay rate. In fact, surface effects contribute to the
modification of the decay properties as well. The interplay of scattering and
absorption in the total decay rate is discussed.Comment: 20 pages, 1 figur
Canonical quantization of macroscopic electromagnetism
Application of the standard canonical quantization rules of quantum field
theory to macroscopic electromagnetism has encountered obstacles due to
material dispersion and absorption. This has led to a phenomenological approach
to macroscopic quantum electrodynamics where no canonical formulation is
attempted. In this paper macroscopic electromagnetism is canonically quantized.
The results apply to any linear, inhomogeneous, magnetodielectric medium with
dielectric functions that obey the Kramers-Kronig relations. The prescriptions
of the phenomenological approach are derived from the canonical theory.Comment: 21 pages, additional reference
Oscillator model for dissipative QED in an inhomogeneous dielectric
The Ullersma model for the damped harmonic oscillator is coupled to the
quantised electromagnetic field. All material parameters and interaction
strengths are allowed to depend on position. The ensuing Hamiltonian is
expressed in terms of canonical fields, and diagonalised by performing a
normal-mode expansion. The commutation relations of the diagonalising operators
are in agreement with the canonical commutation relations. For the proof we
replace all sums of normal modes by complex integrals with the help of the
residue theorem. The same technique helps us to explicitly calculate the
quantum evolution of all canonical and electromagnetic fields. We identify the
dielectric constant and the Green function of the wave equation for the
electric field. Both functions are meromorphic in the complex frequency plane.
The solution of the extended Ullersma model is in keeping with well-known
phenomenological rules for setting up quantum electrodynamics in an absorptive
and spatially inhomogeneous dielectric. To establish this fundamental
justification, we subject the reservoir of independent harmonic oscillators to
a continuum limit. The resonant frequencies of the reservoir are smeared out
over the real axis. Consequently, the poles of both the dielectric constant and
the Green function unite to form a branch cut. Performing an analytic
continuation beyond this branch cut, we find that the long-time behaviour of
the quantised electric field is completely determined by the sources of the
reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field
itself tends to zero, whereas its quantum fluctuations stay alive. We argue
that the last feature may have important consequences for application of
entanglement and related processes in quantum devices.Comment: 24 pages, 1 figur
Time correlations in a confined magnetized free-electron gas
The time-dependent pair correlation functions for a degenerate ideal quantum
gas of charged particles in a uniform magnetic field are studied on the basis
of equilibrium statistics. In particular, the influence of a flat hard wall on
the correlations is investigated, both for a perpendicular and a parallel
orientation of the wall with respect to the field. The coherent and incoherent
parts of the time-dependent structure function in position space are determined
from an expansion in terms of the eigenfunctions of the one-particle
Hamiltonian. For the bulk of the system, the intermediate scattering function
and the dynamical structure factor are derived by taking successive Fourier
transforms. In the vicinity of the wall the time-dependent coherent structure
function is found to decay faster than in the bulk. For coinciding positions
near the wall the form of the structure function turns out to be independent of
the orientation of the wall. Numerical results are shown to corroborate these
findings.Comment: 25 pages, 14 figures, to be published in Journal of Physics
Classical Coulomb Systems:Screening and Correlations Revisited
From the laws of macroscopic electrostatics of conductors (in particular the
existence of screening) taken for granted, one can deduce universal properties
for the thermal fluctuations in a classical Coulomb system at equilibrium. The
universality is especially apparent in the long-range correlations of the
electrical potentials and fields. The charge fluctuations are derived from the
field fluctuations. This is a convenient way for studying the surface charge
fluctuations on a conductor with boundaries. Explicit results are given for
simple geometries. The potentials and the fields have Gaussian fluctuations,
except for a short-distance cutoff.Comment: 17 pages,TE
Kinetic theory of time correlation functions for a dense one-component plasma in a magnetic field
Correlations in a confined magnetized free-electron gas
Equilibrium quantum statistical methods are used to study the pair
correlation function for a magnetized free-electron gas in the presence of a
hard wall that is parallel to the field. With the help of a path-integral
technique and a Green function representation the modifications in the
correlation function caused by the wall are determined both for a
non-degenerate and for a completely degenerate gas. In the latter case the
asymptotic behaviour of the correlation function for large position differences
in the direction parallel to the wall and perpendicular to the field, is found
to change from Gaussian in the bulk to algebraic near the wall.Comment: 24 pages, 10 figures, submitted to J. Phys. A: Math. Ge
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